UKH

My son, 6 years old loves big numbers. I’m looking for more big numbers and analogies for how to explain them to him.

stuff like…

There are more particles in the universe (10^80) than a google (10^100),

There are more stars in the universe than grains of sand on Earth, which doesn’t seem to be true, https://astronomy.com/magazine/bob-berman/2019/01/more-sand-or-stars

We have obviously talked about billions, trillions, quadrillions etc. he had a poster with a million stars on it.

What other big numbers or big number comparisons/analogies should I talk to him about?

Is 10^80 not smaller than 10^100? I don't know, just wondering?

Also it's a googol 🙂

About 3-4 weeks ago my daughter started to realise just how far away stars are and began to take an interest in astronomy.it was like a magic door had been opened to her. She's now convinced that their are aliens out there, but that they're nice. 🙂

Are there more atoms in a cell than there are cells in his body?

Are there more atoms in his body than stars in the observable universe?

The person in that link didn't actually provide the numbers they found so I'm very suspicious. But if you think about how many grains of sand/dust there are on all the planets and moons you'll get a very big number.

Grahams number is big - https://en.m.wikipedia.org/wiki/Graham%27s_number

That link also has links to other large numbers. 

More trees on Earth than stars in our galaxy is one I personally like.

As analogies go, I like using seconds. From memory, a million seconds is about 3 weeks. A billion seconds is over 30 years! That one bends my head a bit, although 30 years might not be relatable to a 6 year old.

I always like the density of neutron stars, 10^17kg/m^3, or as an analogy, 1 teaspoon of neutron star would weigh about a billion tonnes.

Sorry, two typo's in one sentence.

The BBC used to have an awesome interactive graphic for exploring the size of the universe, but looks like its not working any more, anyone know of somewhere we can still access this?
https://www.bbc.com/future/bespoke/20140304-how-big-is-space-interactive/

In his lifetime he will likely earn as much as £2 million.

I also like……there are as much as 180,750 trillion midges in Scotland

I forgot to celebrate both my billionth and 2 billionth birthsecond ☹ although I can remember working out beforehand about when they would be.

Just calculated it again and realised rather despondently that the 2 billionth was just over a month ago. Damn, damn, damn.

A Googleplex is 10^Googol; i.e 10^10^100, which I believe is rather large.

Just how small is an atom...

youtube.com/watch?v=yQP4UJhNn0I&

Brilliant little vid!

I think you just made it worse. Fewer not less, I think. Although who's counting :-P

Avogadro's number is pretty cool. Especially when you think of the comparative volume of a liquid and gas. How many molecules in a gulp of air.

A 6 year old who loves numbers is a wonderful thing. Prime numbers might interest him.

I like that idea. Just put a reminder in my calendar for mine in February!

I went looking for a video I saw a while ago about large numbers, but found this:

youtube.com/watch?v=X3l0fPHZja8&

and also this:

youtube.com/watch?v=5TkIe60y2GI&

Numberphile is addictive.
 

One theory postulates that there are 300 Big Bang neutrinos in every square centimetre of the universe. I’ll let you do the arithmetic on that😀

£44 billion...the amount a billionaire paid in order to trash his investment

Not in the same league but when I was teaching economics, students sometimes had difficulty in appreciating the scale of the sums involved. I used the example of placing a pound coin on a table once every second. It would take approximately 11 and a half days to reach a million pounds but 32 years to reach a billion pounds - you would of course need quite a big table!

To bring that up to date, it would take you just over 76,000 years to place our current national debt...

Might be fun to go the other way - start with a big number and work downwards.  I often use a simplified version of the Drake Equation with students.  Start with the number of stars in the Milky Way, and then say 'what if 1/10 were sun-sized... what if 1/10 of those had planets in the goldilocks zone... what if...'

By the end you can show that there are likely ~10 planets in our galaxy with intelligent alien life.

remember this from your childhood?

Powers of Ten: youtube.com/watch?v=0fKBhvDjuy0&

Not big big numbers but fascinating all the same.

https://www.worldometers.info/world-population/

There's some good stuff mixed into the cartoons at xkcd.com on this kind of thing, and your lad might enjoy some of the 'what if' scenarios.

Here's one about stars and grains of sand: https://what-if.xkcd.com/83/

(And a nice astronomical one about 'angular size': https://xkcd.com/1276/ )

A million seconds is about 11 and half days but yes a billion seconds is over 31 years. The comparison is a great illustration of the comparative size of numbers which isn't immediately obvious.

If we put our minds to it we probably count to a million - if we counted at 1 per second for half of every day(we have to work and eat etc) then it would still be achieveable, but trying to do the same to count to a billion would be unthinkable.

Dave 

That doesn't add up.

1Bn* = 1000x 1M, 1000x 3Weeks = 3000Weeks, 3000/52 ~ 60Years

*Assuming the US and now most commonly used billion (10^9)

If you use the bonkers old UK billion, 10^12 it's ~60,000years!

jk

As I said, I was just relying on memory for the numbers. 

It's already been corrected above that 1 million seconds is 11 days, not 3 weeks, giving us a negligibly greater difference from 31 years. 

Sadly my mum forgot to take her stopwatch to the hospital so I will be denied that pleasure. But then a second is barely time to blow out the candles, so I suppose I won't miss much.

Incidentally, a cake with 2 billion candles would be about half a mile in diameter.

11 days

This is a great toy:

https://htwins.net/scale2/

Not exactly about numbers, but with a similar feel, this is great:

https://eps.berkeley.edu/~saekow/chronozoom/

There was a timeline tool like the scale one above, but I can't fiund it

...and (as per earlier in the thread) ripe for a "what if...?". We have a family legend about some great aunt's 100th birthday. 100 candles on a cake, and after about 70 were lit it turned into a self-sustaining firestorm that coated the whole table with molten wax.

In 9000 BC it’s estimated there were 5 million people on Earth

In 1 AD it’s estimated there were 300 million

The Black Death is estimated to have killed 75 million

In 1650 AD it’s estimated there were 500 million

In 1800 AD, it’s estimated there were a billion 

As of today there are estimated to be 8 billion people on Earth.

if you took a full football stadium and scaled the numbers back to 9000 BC there would be approx 31 fans watching the game.

Maybe I'm being thick....

60sec (1 minute) x 60min (1 hour) x 24 (1 day) x 365 (1 year) = 31,536,000 seconds in a year

1000,000,000 / 31,536,000 = 31.7 years

Yeah, I didn't work back from seconds to weeks, I took that bit at face value and looked at the weeks x1000 to years bit which looked wrong but mostly in order to make the point about the radically different definitions of a billion.

jk

Avogadro's number is indeed a good and important one. I liked to tell my students that there are about a million times more molecules in one gram-molecular weight than the number of seconds that have elapsed in the age of the Universe.

If you manage to spot the Andromeda galaxy (our closest neighbouring galaxy), it's good to tell your children that it has taken 2.5 million years for the light to reach us from there, travelling at 186,000 miles per second!

Good one for understanding powers of 10

youtube.com/watch?v=Hy8VtYYdI9g&

Nope, spot on

At a slight tangent, you could explain numerical patterns, and how they pop up all over the place, e.g Fibonacci.

But best of all, fractals. Instant visual feedback and bright colours.

If you start him now on primes, and multiplying primes, he should be good at cryptography. 2^256 is a big number. Factoring primes in that space will keep him quiet for a while. Also has a direct relevance to computers and the like.

It's harder than this because of the leap year thing. I tried calculating my billionth birth second for ages because I was going to throw a big party or something, but kept getting the calculation wrong. Then I forgot and remembered about it a couple of months later! I'll just have to put the second one in my diary.  

I want to take the kids to a long beach, get a bunch of balls and lay the solar system out to a scale that makes it a few miles long in radius.

So probably needs to be a scale of around a Billion to 1.

At that scale the ball for the earth should be about 13mm in diameter. So a marble.

The sun would be 1.4m. That's  big ball I need to find.

The amount of money a billionaire actually has just blows my mind.

If you were to win £10 million on the lottery every Saturday for your whole lifetime you still wouldn't have enough money for Musks Twitter purchase!

It's obscene.

That's the one I was trying to remember.

I did this last year, it was good fun.  We used a scale of 10 Mkm = 1 step, so Mercury was 6 steps from the sun, Neptune 453 steps, we made a small sandcastle at each planet and imagined going on visits to each planet.  I didn't bother making the sandcastles to scale as you point out the Sun would be massive and all the others tiny.

On this scale the orbit of Neptune was nearly 3km long, so we didn't plot out the orbits of the bigger planets, but to do so would be a good workout.

Grains of rice on a chess board is good.  One on the first square, 2 on the second, 4 on the third...

2^64 on the last - more than grains of sand on earth

This is the most interesting thing I've read all week and definitely the biggest number in this thread! Who knew there was something called Busy Beaver numbers.

Who knew there was a number that was so big you can't even begin to write it down with all the available volume in the universe... but that we've thought of a notation to do just that. Super interesting.

Spoiler alert for the Book Contact

I'll never forget reading the epilogue of that book when I was younger and seeing the super computer find the perfect circle in the digits of Pi, then it made me think surely all that is knowable in the universe is encoded in the digits of Pi, by definition, and that blew my mind. Pseudo-science for sure but nevertheless. Had more time for thinking these esoteric thoughts when I was younger.

A version that I was told about by a maths teacher is that a zombie can convert one victim per day. The apocalypse starts on the 1st of January - on what date is the last person in Scotland zombified?

Follow up with what date was half the population still human?

(Yes I know that there is a smart answer to that with a hint of truth on Ne'er Day)

https://plus.maths.org/content/too-big-write-not-too-big-graham#:~:text=Gra....

but not more than the number of bits required completely to describe all of those grains of sand - now that's what I call a big number!

I think we have to accept that even with accurate timekeeping, birth takes more than one second, so a billionth birthsecond etc will have to be only nominally around the right time (i.e. get the leap years correct and BST/GMT but not more than that).

No. Graham's number is a big number

I believe some American did this, took about 2 or 3 months I think. Articulating the big numbers must take a while.

We really enjoyed both of those, thanks. Particularly the scale of the universe. ‘Zoom out! Zoom out!’

There's a great u tube video where a guy illustrates that using grains of rice. I had a quick look but didn't find it. I'll have another look.

Graham's Number? Pah! Tree(3) is where it's at.

youtube.com/watch?v=IihcNa9YAPk&

Go down to the beach. There are as many (I dunno really, could be a factor of 10 or so either way. Depends how big the beach is and how far down the sand goes) atoms in a grain of sand as there are grains of sand on the beach.

I just came across this, which details all the big numbers there are (pretty much).

youtube.com/watch?v=RJS3Z2DYEO4&

 

Infinity is a great topic if you want big numbers.

Veritasium --  youtube.com/watch?v=OxGsU8oIWjY& -- "How An Infinite Hotel Ran Out Of Room"

Tree(3)+1

Tree(4)

The original claim was more stars in the universe than grains of sand on beaches, which does seem to be likely true, as confirmed in the same article (numbers of stars in the observable universe are close).

Lawrence Krauss has a nice big number example in The Physics of Star Trek, where he considers the challenge of devising a 'Beam me up Scotty'-type transporter.

Leaving aside the question of transporting actual atoms, and just considering it as a data transmission problem, then we might estimate that it takes, say, a kilobyte of data to record everything we need to know about each atom in a human body, and here are 10^28 or so of them. 

If safety from the Klingons or other galactic nasties requires transmission of this data within a second, then if we assume maximum possible bit transmission rates increase by.a factor of 10 every decade, we can work out how long it will take from what we can do now to what we need to be able to do. A couple of centuries or so. 

Doesn't seem so far off!

That would need a relative coordinate system (each atom positioned relative to another atom) and not absolute.  I sure hope the encoding algorithm tracks the quantisation errors and eases them holistically, otherwise there’s going to be one hell of a snap, crackle and pop when someone rematerialises.

Well, I may have glossed over a few technical details.

I think the Heisenberg compensators take care of that. 

The whole spirit of Star Trek and other such sci fi  is that we gloss over inconvenient technical details and just assume that that they have worked them out, somehow. I always wondered how they could go to warp speed, just like that, without Uhura, Spock, Bones, Kirk and the rest being splattered over the back wall of the command deck. 

My thought was always, if they can teleport, why aren't they replicating?

Or maybe quantum entanglement somehow prevents that.

They do sometimes, if it's a handy device to tell the story the writers want to tell.  Commander Riker had a doppelganger who was stranded on a planet somewhere for years because when the crew thought they'd beamed him up to the ship he was on at the time they'd accidentally replicated him instead, rescuing one copy and leaving the other one behind.

It's a Ship of Theseus/Trigger's Broom paradox - if transportation involves disintegrating you at one end and making an exact replica at the other, is it still you that arrives?

They try to keep the 'rules' broadly consistent but I think the writers of individual episodes can get away with bending them a bit.  The producers don't care as long as it's only the geeks that notice.

The thing that always bothered me was when something had to be timed to the precise millisecond or the ship would explode or whatever - they always achieve that precise millisecond timing by one person on the bridge looking at a screen and shouting "now!" for someone else on the other side of the bridge to press a button.

Tree(tree(tree(tree....(tree(3^tree(3))))

I watched a video on it but they never came close to actually explaining how big the number is, just that it's too big to be represented in this universe with our normal number system.

Read somewhere recently that the voyager space craft, that is currently the furthest man made object from Earth, will take 18,000 years to travel one Light year, Seeing as the nearest star to us is 4.35 light years away, I think we need to find some faster spacecraft

waiting for someone to fact check my figures : )

Do you remember where it came from? This sounds like something my nephew would love!

An interesting way of getting a huge number from a relatively small number is factorials. 

For example, if your son is in a class of say 30 children and they all had to line up in the playground, in how many different ways (orders) can this be done?
As there are 30 possible choices for the first child, 29 for the second, down to 1 for the last, the total number is 30x29x28x...x1, or 30! (factorial) which is approx 2.65 x 10 to the power 32, or 265 million million million million million.

Another good example, which I'm sure has already been mentioned, if the chessboard and rice story: 
https://www.mathscareers.org.uk/the-rice-and-chessboard-legend/

It's in the back of a book called 'How Big Is A Million' it features a penguin finding 10 fish, 100 penguins, 1000 snow flakes and then 1 000 000 stars.  Then the poster is folded up in the back.

Nice book but probaby more suited to 3 year olds than 5-6 year olds.

Is that Graham's number?

Reminds me of something I heard that allegedly happened at a Star Trek convention. Actors, writers, advisors and various production crew members were there taking questions from an audience.

One person asked how the Enterprise could slow down safely so quickly, to which one the Star Trek team said, "The Enterprise uses inertial dampers". The follow up question was, "How do the dampers work?" To which the answer was, "They work very well."  

Dave

Space is being warped around them, they aren’t travelling FTL through space. It’d be interesting to know their actual speed through the warped space.

I think there are loads, Graham's, Tree(3+) etc.

It's obvious when you think about it I suppose but I did a physics degree so used to seeing numbers like Ax10^38 etc. but the thought of a number that you can't even fit on a page, let alone in all the planck volumes in the universe, using this kind of notation is mind blowing (though obvious when you think of numbers going up to infinity).

"Leaving aside the question of transporting actual atoms, and just considering it as a data transmission problem, then we might estimate that it takes, say, a kilobyte of data to record everything we need to know about each atom in a human body, and here are 10^28 or so of them. "

that is what I was getting at in my comment about a large number earlier.

Look up Graham's number. From memory it's an upper bound to some algorithm. It is too big to be expressed a "power tower" (e.g. 10^10^10^10... etc) even if every digit was the size of an atom

There have been some very big number suggestions up thread, Graham, Tree(3), and so on - which I can't begin to think how to explain to my son. 

I've had some great conversations with the lad about the scale of the universe slider interactive graphic and enjoyed trying to explain to him that even if you turned every atom in the universe into zeros you woudn't have enough to write down a googolplex.  When I get chance I'll get a grain of sand and try to explain to him that there are more atoms in a grain of sand than there are on an average beach so thank's for all the contributions.

I'm currently reading 'Fantastic Numbers and Where to Find Them' which is great and i'm looking forward to learning a bit more about infinity which I can distill down to him.

I love talking to students about received signal powers, I was just checking voyagers for you and if you scroll down this link you can see both the received and transmit powers to talk to them.  I normally start in dBm (~ -245dBm in 2013) and then changing it to milli watts with all the zeros and putting that into words.

https://space.stackexchange.com/questions/9824/how-much-rf-transmit-power-d...

Cheers

Toby

There goes another one!

This reminds me of a serious conversation between colleagues that I once overheard on dilithium crystals. 

It was a contraction of typographicalerrors

I've got a 2nd hand copy of a book called 'A Hundred Billion Trillion Stars' which is pretty good. Lots of big numbers in there, number of trees, stars, gallons of water, that sort of thing.

What a brilliant thread!  Made me laugh out loud at times with the joy of some of the very large numbers!

Recently I was explaining compound interest to my granddaughter. She’ s interested in bacteria at the moment (they have captured her imagination) so we calculated starting with one which divides and reproduces every 20 minutes. Assuming enough food and no deaths how many after 24 hours. We then looked up a typical mass for one bacterium (about 10^-12 g) and worked out the mass of all our bacteria after only 24 hours. She’s 12 so the sums were within her capability with a bit of help. She was truly astonished at the result . 

I'm fascinated, as a non-mathematician, to know what 'more' one can learn about infinity. To me it seems to be exactly what it says, literally ad infinitum. I'm half expecting scientists here to leap back and say it's got some shape, or something equally weird.

Google for 'Cantor' and 'Infinity', Gordon.

In summary: there are multiple levels of infinity. Beyond that, there are very deep and  unanswered questions.

Careful what you wish for…

Infinities have different sizes…

The natural numbers 1, 2, 3, etc are infinite. The rational numbers 1/2, 1/3, 3/4 etc are infinite. Both of these infinities can be shown to be the same ‘size’.

The real numbers 0.2, 1.34, 999.999999 etc are infinite. This infinity is bigger than the previous one.

Beat me!

Hate to say it, but I'm so much more concerned about problems on Planet Earth right now, quite frankly.

Ummmmmmmmmmmmmmmmmmm (that's going to infinity, BTW.)

I'm seriously/cheekily wondering, given that numbers exist in a virtually separate Platonic world of their own, how much this actually means. Also, sorry, I can't get out of my head the idea of a comic sketch setting those words above to music.

Sorry, I guess I'm really thick, but how can "the previous" infinitely big infinity – sorry, can't help chuckling – be "smaller" than the present infinitely big one? The word surely means what it says?

That's fine. I was only replying since you appeared to be expressing a genuine interest.

I'm interested in an academic way, but have to confess I'm kind of lost on it. 

This link is way quicker than me typing, and I’m needing to catch up on my Zs. Good night and enjoy.

https://www.sciencealert.com/here-s-the-simple-proof-that-there-must-be-mul...

edited cos I forgot to include the link. Sleep beckons.

Thanks.

The infinite hotel paradox is quite fun, the kid might enjoy that if they get to infinity. There's are several versions, here's one:

Hotel Infinity has an infinite number of rooms, and it's currently fully booked with an infinite number of guests staying there.  An infinite coach turns up and the driver says she's sorry about the short notice but they've just missed a ferry and can they somehow squeeze her infinite number of passengers into the already full hotel.

No problem says the receptionist, and sends a message to all the existing guests asking them to double the number of their current room and move to that one. And voila! All of the odd-numbered rooms are now free, so the infinite number of new guests can move into those.

Quite a pivot in 5 minutes, did you make yourself dizzy?

For lovers of Trivial Pursuit the 27th meeting of the General Conference on Weights and Measures has just decided to add four new official SI prefixes for multiples of 10 for everyone to learn;

ronna R  =  10^27 , ronto r = 10^-27, Quetta Q = 10^30, quecto q = 10^-30

https://www.bipm.org/documents/20126/64811223/Resolutions-2022.pdf/281f3160...
(The English translation comes after the French)

The conference also decided to work on redefining the second, as the current definition isn’t as good as it could be, and to ditch the leap second for something else yet to be decided.

As if life wasn’t complicated enough already!

And yet… the hotel remains the same ‘size’.

Beat me to the recommendation for Numberphile! Hard to beat the TREE(3) video.

OP: you could try some real life exercises to generate modestly large numbers. Like, number of possible ways to shuffle a deck of cards.

I had a nice encounter with a large number at work last year. Our call routing system can be configured to route different types of calls to different queues, and then different teams of people can take calls from combinations of different queues. The way these combinations are coded is pretty simple and easy to manage for a small number of options. The operations team wanted to add a whole bunch of different call types, queues, and teams. After doing the maths I had to explain why that wasn't possible without designing a new custom system to handle the routing: "you've asked for a system that can handle more possible combinations than there are atoms in the Sun, and the system has a limit of 200"

Rubbish, Iv'e had that many in my tent!

£s or Midges?

There are roughly 50 billion red blood cells in his blood and 5 billion white blood cells in his blood.

Out of date - Root1's midges have called by